Overview
Discover how multi-stage neural networks can achieve machine precision for scientific problems, overcoming traditional accuracy limitations and addressing spectral bias in multiscale dynamics and fluid dynamics.
Syllabus
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- Introduction to Neural Networks
-- Overview of Neural Network Architectures
-- Understanding Neural Network Training and Optimization
-- Limitations of Traditional Neural Networks in Scientific Problems
- Fundamentals of Multiscale Dynamics
-- Definitions and Characteristics of Multiscale Problems
-- Challenges in Fluid Dynamics and Spectral Bias
- Machine-Precision Concepts
-- Achieving Machine Precision in Neural Networks
-- Precision Metrics and Evaluation Methods
- Multi-Stage Neural Networks
-- Architecture and Design of Multi-Stage Networks
-- Training Techniques for Multi-Stage Structures
-- Case Studies: Applications in Multiscale and Fluid Dynamics
- Overcoming Spectral Bias
-- Understanding and Identifying Spectral Bias
-- Techniques for Mitigating Spectral Bias in Neural Networks
- Precision Optimization Techniques
-- Advanced Optimization Algorithms
-- Techniques for Increasing Numerical Precision in Networks
-- Comparison of Precision Techniques in Scientific Problems
- Case Studies and Applications
-- Real-World Applications in Fluid Dynamics
-- Exploring Multiscale Dynamics Solutions
-- Analysis of Results and Machine Precision Achievements
- Hands-On Workshop
-- Practical Session: Building a Multi-Stage Network
-- Performance Analysis: Evaluating Machine Precision on Test Cases
- Advanced Topics (Optional)
-- Recent Advances in Neural Networks for Scientific Computing
-- Future Directions in Machine-Precision Networks
- Conclusion
-- Recap of Key Concepts
-- Emerging Trends and Continued Learning Paths in Neural Networks for Scientific Applications
Taught by
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On-Demand
